The goal is to develop mathematical models of the blood flow and transcapillary exchanges in capillary networks. Effort is being made to incorporate in the models the histological structure of capillary networks as well as different flow patterns from available experimental information. In this model the extraction of substrates with different chemical kinetics at the tissue site will be described. It is expected that this could be used in experimental situations where the extraction of different substrates are measured simultaneously, thus helping to infer the flow pattern features of the microcirculation. In particular a model of the diffusion-consumption of oxygen in striated muscle containing myoglobin (facilitated diffusion) is being developed and pertinent numerical results examined. A possible adaptive mechanism for the facilitated transport of oxygen by hemoglobin in nematodes (Ascaris lumbricoides) and myoglobin in vertebrate striated muscle has been investigated.